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Becoming a GMAT Even-Odd Champion: Q2

Question 2

If P and Q are positive integers, is the product 3PQ divisible by 2?

  1. 6Q3 + 2 is an even number
  2. P + 8Q2 is a prime number

Correct Answer



Steps 1 & 2: Understand Question and Draw Inferences

3PQ is divisible by 2, if:

  • 3PQ is even

–>  PQ is even (Odd term 3 plays no role in the even-odd nature of product 3PQ)

–>  P is even (Power doesn’t impact the even-odd nature of a term)


So, to answer the question we need to find if P is even


Step 3: Analyze Statement 1

6Q3 + 2 is an even number

Not Sufficient. We do not know if P is even or odd


Step 4: Analyze Statement 2

P + 8Q2 is a prime number

All the prime numbers except 2 are odd

–>  As Q ≠0, P + 8Q2> 2      (Given: Q is a positive integer => Q >0)

–>  P + 8Q2 is always odd

8Q2 is always even

–>  P must be odd                                                                                  (Odd + Even = Odd)



Step 5: Analyze Both Statements Together (if needed)

We get a unique answer in step 4, so this step is not required


Answer: Option (B)


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5 thoughts on “Becoming a GMAT Even-Odd Champion: Q2”

  1. Hey, how can the answer be B. B gives us information about P whereas 3PQ can be divisible by 2 if Q is even and P is odd. Since we have no information about Q, should the answer not be E?

  2. Hi , For statement 2, I understand Q is a positive integer i.e. Q >0, however how did we deduce that P + 8Q^2> 2 ??

    1. Hi JIA,
      If you look at the question, it said P+8Q”2 is a prime number. All prime numbers are odd except for 2 hence the expression P+8Q”2 > 2 because we know that it cannot be equals to 2. The trick is focusing on the constraints in the question. Once you get that out of the way you can deduce that 8Q”2 will always be even leaving P to definitely be odd.

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Co-founder, e-GMAT
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